A375660 Expansion of e.g.f. 1 / (1 - x * (exp(x) - 1))^2.

1, 0, 4, 6, 80, 370, 4152, 34034, 413632, 4744674, 66354680, 954512482, 15454225536, 263909265074, 4898255210968, 96284064551250, 2022022344889472, 44858682139345090, 1052826609589372152, 25994393541984673154, 674563101823606851520, 18337775305498096349202

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052848.

a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)! * Stirling2(n-k,k)/(n-k)!.

Mathematica

With[{nn=30}, CoefficientList[Series[1/(1-x*(Exp[x]-1))^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 13 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*(exp(x)-1))^2))
(PARI) a(n) = n!*sum(k=0, n\2, (k+1)!*stirling(n-k, k, 2)/(n-k)!);

Crossrefs

Cf. A052848, A375661.

Cf. A005649.

Sequence in context: A197315 A061216 A058163 * A303211 A264374 A013127

Adjacent sequences: A375657 A375658 A375659 * A375661 A375662 A375663

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2024

Status

approved